Debt - Credit Agreement - Additional Information (Details) - USD ($)	3 Months Ended		9 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021	Aug. 02, 2022	Feb. 13, 2020
Debt Instrument [Line Items]
Credit facility amount						$ 1,000,000,000
Voting interest in domestic subsidiaries pledged against credit facility			100.00%
Voting interest in foreign subsidiaries pledged against credit facility			65.00%
Leverage ratio, actual	0.0197		0.0197
Senior debt leverage ratio, actual	0.0061		0.0061
Fixed charge coverage ratio, actual	0.1374		0.1374
Periodic interest payment	$ 2,100,000	$ 3,200,000	$ 25,900,000	$ 23,700,000
Interest rate during period	3.40%	3.10%	3.30%	3.40%
Foreign Subsidiary | Subsequent Event
Debt Instrument [Line Items]
Long-term portion of long term debt					$ 0
Line of Credit
Debt Instrument [Line Items]
Line of credit facility, maximum borrowing capacity expansion amount						$ 500,000,000
Credit facility maturity date			Feb. 13, 2025
Basis spread on Federal Reserve Bank of New York (FRBNY) rate	0.50%		0.50%
Basis spread on adjusted LIBOR			1.00%
Investment limit in foreign subsidiaries	$ 100,000,000		$ 100,000,000
Cash investment limit for acquisition of business	$ 200,000,000		$ 200,000,000
Total leverage ratio	4.50		4.50
Senior secured leverage ratio	3.00		3.00
Minimum fixed charge coverage ratio allowed under debt covenant	3.00		3.00
Line of Credit | Minimum
Debt Instrument [Line Items]
Variable interest rate, length of time between updates			30 days
Credit facility commitment fees percentage			0.175%
Line of Credit | Minimum | London Interbank Offered Rate (LIBOR)
Debt Instrument [Line Items]
Basis spread on variable rate			1.25%
Line of Credit | Minimum | Base Rate
Debt Instrument [Line Items]
Basis spread on variable rate			0.25%
Line of Credit | Maximum
Debt Instrument [Line Items]
Variable interest rate, length of time between updates			180 days
Credit facility commitment fees percentage			0.30%
Line of Credit | Maximum | London Interbank Offered Rate (LIBOR)
Debt Instrument [Line Items]
Basis spread on variable rate			1.75%
Line of Credit | Maximum | Base Rate
Debt Instrument [Line Items]
Basis spread on variable rate			0.75%
Secured Debt | Revolving Loan, Reset Period One
Debt Instrument [Line Items]
Annual rate for borrowings outstanding	2.67%		2.67%